Posts Tagged ‘streak’
When You’re “Due” — The Gambler’s Fallacy
I travel to Las Vegas once or twice a year, both to play poker (where I convince myself I have an advantage) and to dabble in other games (where I definitely don’t). Since 1993, when I started playing while on the East Coast, I’ve seen thousands of players succumb to the insidious gambler’s fallacy.
Let’s say you’re playing roulette and notice, as posted on the so very helpful display by the wheel, that five red numbers have come up in a row. Is black due? What about green (0/00)? The answer is neither. Roulette wheels are well-balanced and the little obstacles spread around the wheel, called canoes in casino parlance, make outcomes random enough to be considered independent trials. If red numbers come up five times in a row, the next number will be red 18/38 of the time, black 18/38 of the time, and green 2/38 of the time. Ironically, it’s our human urge to discover patterns that makes the gambler’s fallacy work. The wheel has no memory, but we do.
The bottom line is that when you play roulette, the proportion of red, black, and green numbers will tend toward the target ratios over millions of spins and the weighted payoffs will ensure the house earns its profit over the long run. But what about games like poker? Poker is a skill game with a healthy dose of luck thrown in, so trials aren’t truly independent. Inferior players beat better players over the short term, but only because of luck. But what happens when equal players face off?
It’s hard to find players of the same skill level at a poker table, but I tested the theory by replicating an experiment described by poker author Lou Krieger. Like Lou, I set up ten identical players in Wilson Software’s Turbo Texas Hold’em simulation mode and let them play hundreds of millions of hands against each other. Six of the ten players were just above or below breaking even, but there were two big winners and two big losers. Remember that each player followed an identical strategy — the only factor controlling their fate was the luck of the draw.
As human beings trying to extract a living from an indifferent universe, we must realize that the odds are not always in our favor and that we will go through bad streaks we can’t seem to reverse. At these times it pays to strengthen your base by learning new skills or practicing old ones, reinforcing friendships, reaching out to others for help, and offering assistance where you can. Doing these things doesn’t constitute “good karma” or “putting things out into the universe”, both dubious concepts. What you are doing is improving the chances you’ll be ready to take advantage of opportunities that you and your contacts discover.
Clustering and Streaks — Real or Imagined?
The folk wisdom that “bad things come in threes” is still popular in the U.S. Whenever two celebrities die on the same day, for example, even the most hardened critical thinker feels the urge to look for the third.
Is clustering real? Do events happen in streaks, or are they just a product of our pattern-seeking brains? George Carlin made fun of the “bad things happen in threes” adage by stating that bad things actually happen in 27’s, noting that “it just takes longer to see the pattern.” You can always find instances of “bad things” in the world to fill out your sets of three, but what does the research say? There have been a lot of studies on the subject, including Koehler and Conley’s “The “Hot Hand” Myth In Professional Basketball”, published in 2003 in the Journal of Sport and Exercise Psychology. The authors examined the National Basketball Association’s long distance shooting contest and looked for statistical aberrations in the sequences of made and missed shots. As in all but a few other studies, they found no significant deviation from chance. When they took each player’s base shooting accuracy into account, the effect disappeared.
Sports are physical contests and even little variations in physical conditions can affect performance, but what about chess? Chess is a mental game played with perfect information. That is, you know everything there is to know about a position and there’s no hidden information, such as a player’s hole cards in poker. As of this writing, I have played 19,738 games of blitz chess (each player has 3 or 5 minutes to make all moves in a game) at the Internet Chess Club since June 27, 2001. As I watch my online chess rating fluctuate from embarrassing to “not bad for me”, I wonder how much the streaks of wins, losses, and draws reflect my abilities and how much is the “luck” of an opponent making some horrible mistake.
The three-year graph of my rating shows huge swings, but the average is right about where I perceive myself as a player. Perhaps my streaks are due to luck. After all, I don’t seriously study the game and play to take a break from other work. The big changes make a strong visual impression, but there are a lot of small shifts in there, too.
Improvisers can make a fun game out of looking for apparent patterns and justifying reasons for believing streaks exist. The lesson for analysts? Carefully examine whether a sequence of events is due to some underlying cause or is just a sequence of events that might be due to chance. That said, given the strength of our innate need to discover patterns, is there any way to dispel what appears to be the myth of the hot hand? In a 2006 review of the literature, Michael Bar-Elia, Simcha Avugosa, and Markus Raab summarized the situation in this way:
As Amos Tversky, who initiated the hot hand research, used to say (cited by Gilovich in an online chat, September, 2002), ‘‘I’ve been in a thousand arguments over this topic, won them all, but convinced no one’’.
Improspectives 